A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of…
A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is
$1 / 15$
$2 / 5$
$4 / 15$
$7 / 15$
Solution
The number of ways to select 2 balls out of 10 $={ }^{10} C_2$
Number of ways to select 2 balls both white $={ }^6 C_2$.
Number of ways to select 2 balls both black $={ }^4 C_2$
$\therefore$ The required probability $=\frac{{ }^6 C_2+{ }^4 C_2}{{ }^{10} C_2}=\frac{7}{15}$